Eur J Appl Physiol (1990) 61:453-460

European

Applied Physiology and Occupational Physiology © Springer-Verlag 1990

Length and moment arm of human leg muscles as a function of knee and hip-joint angles J. J. Visser, J. E. Hoogkamer, M. F. Bobbert, and P. A. Huijing Vakgroep Functionele Anatomic, Faculteit Bewegingswetenschappen, Vrije Universiteit, van de Boechorststr. 9, NL-1081 BT Amsterdam, The Netherlands Accepted May 29, 1990

Summary. Lengths of muscle tendon complexes o f the quadriceps femoris muscle and some of its heads, biceps femoris and gastrocnemius muscles, were measured for six limbs o f h u m a n cadavers as a function o f knee and hip-joint angles. Length-angle curves were fitted using second degree polynomials. Using these polynomials the relationships between knee and hip-joint angles and m o m e n t arms were calculated. The effect o f changing the hip angle on the biceps femoris muscle length is m u c h larger than that of changing the knee angle. For the rectus femoris muscle the reverse was found. The m o m e n t arm of the biceps femoris muscle was found to remain constant throughout the whole range o f knee flexion as was the case for the medial part of the vastus medialis muscle. Changes in the length of the lateral part of the vastus medialis muscle as well as the medial part of the vastus lateralis muscle are very similar to those of vastus intermedius muscle to which they are adjacent, while those changes in the length of the medial part of the vastus medialis muscle and the lateral part of the vastus lateralis muscle, which are similar to each other, differ substantially f r o m those of the vastus intermedius muscle. Application o f the resuits to j u m p i n g showed that bi-articular rectus femoris and biceps femoris muscles, which are antagonists, both contract eccentrically early in the push off phase and concentrically in last part of this phase.

Key words: Muscle length changes - Joint angle - Moment arm - Lower limb

Introduction With the present interest in modelling the skeletomuscular system of the lower extremities (e.g. Gregoire et al. 1984; Bobbert et al. 1987), it is desirable to quantify the relationship between the length o f the muscle ten-

Offprint requests to: P. A. Huijing

don complexes and joint angles. This is particularly important for poly-articular muscles for which even the direction of length change is u n k n o w n during some specific movements, due to the opposing effects on muscle length o f changes of the angles o f the joints they span. Frigo and Pedotti (1978) schematized the l o c o m o t o r apparatus by modelling muscles as linear connections between the midpoints of their origins and insertions. Joints were represented as hinges. This simplification allowed the calculation of estimates of m o m e n t arm and length changes in the muscle tendon complex. Grieve et al. (1978) studied such length changes o f the triceps surae muscle in the lower limbs of h u m a n cadavers. Their methods avoided any of the simplifications of muscle and joint geometry, as well as a choice o f axis of rotation. In the present work, these methods were applied to other leg muscles with the aim of determining lengths o f the heads of h u m a n quadriceps femoris muscle, of biceps femoris muscle and of gastrocnemius muscle as a function of lower limb joint angles.

Methods Experimental procedure. The study was performed on six legs of five human cadavers (two males, three females). The limbs were separated from the rest of the body at the level of the fourth lumbar vertebra. The pelvis was separated in the median plane. Skin, fascia lata and muscle fascia were removed. The quadriceps femoris muscle, biceps femoris muscle (BF) and gastrocnemius muscle (G) were dissected. Of the quadriceps muscle the following parts were distinguished: rectus femoris muscle (RF), vastus intermedius muscle (VI), vastus medialis muscle medial part (VMM) and lateral part (VML) and vastus lateralis muscle medial part (VLM) and lateral part (VLL). The muscles studied were cut transversely at standard locations (Table 1). Other muscles that did not influence the position of the muscles studied were removed. Those muscles that, if removed, would have influenced the muscles studied were left in position but were cut to make joint movement possible. To obtain sufficient range of motion of the knee and hip joints, small incisions were made in the joint capsules. Subsequently Bandafix, a wide mesh elastic gauze bandage, was slipped

454 Table 1. Locations of transverse section of muscles Rectus femoris: Vastus medialis: Vastus lateralis: Vastus intermedius: Gastrocnemius: Biceps femoris:

10 cm distal of spina iliaca anterior inferior, and 2 cm proximal of basis patellae 3.5 cm proximal of basis patellae 4 cm proximal of basis patellae 5.5 cm proximal of basis patellae 10 cm proximal of insertion on the calcaneus 10 cm distal of tuber ischiadicum, and 13 cm proximal of insertion at caput fibulae

b

chanter major and the most distal aspect of the epicondylus lateralis femoris with the line connecting the most lateral aspect of the malleolus lateralis and the most proximal aspect of the condylus lateralis tibialis was 0% This position was referred to as 0 ° of knee flexion. For the hip joint, the reference position was defined by imposing an angle of 15 ° between the line connecting the spina iliaca anterior superior and the spina iliaca posterior superior and the vertical line. This position was referred to as 0 ° of flexion. In the reference position, the line between the spina iliaca anterior superior and the apex patellae (frontal plane) was maintained parallel to the sagittal plane. A diagram of the experimental set-up is shown in Fig. lb. Changes in hip-joint angle were brought about by moving a board with the pelvis firmly attached to it along another board that was part of the frame. Changes of knee-joint angle were made by allowing gravity to bend the leg, by easing off a cord connecting the tibia and the frame. With respect to the reference angles in the standard position the knee-joint angles studied ranged from 0 ° to 90 ° of flexion for the knee and from - 15 ° to 60 ° of flexion for the hip. Knee- and hip-joint angles were changed in steps of approximately 5 ° as indicated by a goniometer. A photographic slide was taken at each position. In postexperimental analysis of the slides, the exact angle was determined. As the angle of one joint was varied, the other joint was fixed in the standard position. The distances between the edges of the transverse cuts of each muscle or head at each joint angle represent ALoi, the length of the muscle tendon complex relative to reference length. These distances were measured using a pair of compasses, a ruler and a Vernier caliper. For the vastus lateralis and medialis muscles these distances were determined at both the medial and lateral edges of the cut. Lengths were expressed as percentages of the segment length. Upper segment length was defined as the distance between the most lateral part of the trochanter major and the most distal point of the condylus tateralis femoris. Lower segment length was defined as the distance between the most proximal point of the epicondylus lateralis tibialis and the lateral tip of the malleolus lateralis. Segment lengths are shown in Table 2.

Analysis of data. The raw values for length of the muscles were fitted with a second degree polynomial by a method of least squares (Business Graphics, Apple Inc.): Fig. 1. Diagram of experimental set-up, a Positions of markers on the lateral side of the leg: 1, spina iliaca anterior superior (SIAS); 2, spina iliaca posterior superior (SIPS); 3, extra marker for determining hip joint angle; 4, most lateral aspect of trochanter major; 5, most lateral aspect of malleolus lateralis; 6, most distal aspect epicondylus lateralis femoris; 7, most proximal aspect condylus lateralis tibialis; 8, middle part of patella; 9, tuberositas tibiae; 10, extra marker for determining knee joint angle; 11, line between markers on trochanger major and malleolus lateralis, used for setting the reference position of the leg; 12, line between SIAS and SIPS; 13, vertical line (i.e. horizontal line when standing erect); in the reference position, an angle of 15 ° existed between lines 12 and 13. b Mounting frame and methods of changing joint angles: 1-4, damps fixing the femur; 5, pulley; 6, plastic board attached to the pelvis; 7, part of reference frame

dlo~ = Ao + A1 Oi + A2 (Oi)2 where Aloi represents the origin to insertion length relative to length in the reference position (as percentage of segment length) and Oi represents joint angle (in degrees); A0, A1, and A2 are constants. Muscle moment arms as a function of knee and hip joint angles were calculated, according to Bobbert et al. (1987) by the following equation: d = (A1 + 2 A2 O/) × 180/rt where moment arm (d) is expressed as a percentage of segment length and ~9~ is expressed in degrees; A1 and A2 are the same constants as above.

Table 2. Segment lengths of six limbs of five human cadavers around the leg to hold the muscles together, much like a general fascia.

Cadaver Upper segment length Lower segment length (mm) (mm)

Experimental set-up. The legs were mounted in a special frame which had been constructed for this study. The femur was clamped to the frame, while the tibia and pelvis could be moved. The leg was positioned in the reference position corresponding to the posture of standing erect using markers on the frontal and lateral sides of the leg (Fig. l a). In the reference position, the angle between the lines connecting the most lateral aspect of the tro-

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Length and moment arm of human leg muscles as a function of knee and hip-joint angles.

Lengths of muscle tendon complexes of the quadriceps femoris muscle and some of its heads, biceps femoris and gastrocnemius muscles, were measured for...
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